# Matter Waves (Wave Particle Duality)

Special relativity said that

if m=0

Plank said he could fit the Black Body radiation data assuming that that

where = Plank's constant

Combining the two we have

photons have momentum like a particle (mv)

Do particles reciprocate and behave like photons?

## De Broglie's Hypothesis

If photons can behave like particles by having momentum

Then can a particle behave like a wave by having wavelength

or

de Broglie Hypothesis

## Davisson and Germer

We know that X-rays having a wavelength of make an interference patter on an aluminum foil.

Another way to calculate

What would be the energy of an electron with the same wavelength as the above X-ray?

relativistic total energy relation

= 511.3 keV

relativistic kinetic energy

Note classical physics may be used for electrons below 50 keV
K = \frac{1}{2} mv^2 = \frac{1}{2}\frac{511 \mbox{keV}}{c^2}(0.03 c^2 =

Hit a crystal made of nickel with 54 eV electrons.

1.) 54 eV electrons

From hyperphysics: